Use an Indirect Proof to Complete the Following Problem

Question

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The Answer is Suppose that Suppose that and are both obtuse angles. Then and . It follows that . But it is given that and are supplementary, so that . With a contradiction of the known fact, it follows that the supposition must be false; thus, and are not both obtuse angles.

Suppose that and are both obtuse angles. Then and . It follows that . But it is given that and are supplementary, so that . With a contradiction of the known fact, it follows that the supposition must be false; thus, and are not both obtuse angles.

and

are both obtuse angles. Then Suppose that and are both obtuse angles. Then and . It follows that . But it is given that and are supplementary, so that . With a contradiction of the known fact, it follows that the supposition must be false; thus, and are not both obtuse angles.

and

.
It follows that Suppose that and are both obtuse angles. Then and . It follows that . But it is given that and are supplementary, so that . With a contradiction of the known fact, it follows that the supposition must be false; thus, and are not both obtuse angles.

. But it is given that Suppose that and are both obtuse angles. Then and . It follows that . But it is given that and are supplementary, so that . With a contradiction of the known fact, it follows that the supposition must be false; thus, and are not both obtuse angles.

and

are supplementary, so that Suppose that and are both obtuse angles. Then and . It follows that . But it is given that and are supplementary, so that . With a contradiction of the known fact, it follows that the supposition must be false; thus, and are not both obtuse angles.

.
With a contradiction of the known fact, it follows that the supposition must be false; thus, Suppose that and are both obtuse angles. Then and . It follows that . But it is given that and are supplementary, so that . With a contradiction of the known fact, it follows that the supposition must be false; thus, and are not both obtuse angles.

and

are not both obtuse angles.

Use an Indirect Proof to Complete the Following Problem

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